Learn Hardcore German: Nach dem Unterricht stehen viele Studenten an der Kreuzung und suchen die richtige Richtung. - After class many students stand at the intersection and look for the correct direction.

The preposition nach always takes the dative case. Unterricht is masculine (der Unterricht), and in the dative the article der changes to dem, giving nach dem Unterricht.

Why is the verb stehen used here instead of something like sitzen or gehen?

stehen literally means “to stand,” indicating that the students are upright, perhaps waiting or lingering. sitzen would mean they are seated; gehen would mean they are walking. Choose stehen when you want to stress that they remain on their feet in one place.

Why is it an der Kreuzung and not in der Kreuzung or auf der Kreuzung?

The preposition an with the dative case conveys “at” a point or boundary (like a shore, wall, or intersection). A crossroads is a specific point where streets meet, so you stand an der Kreuzung (“at the intersection”). in der Kreuzung would imply inside the intersection, which doesn’t make sense; auf could be used for surfaces (like “on the square”), but not for intersections.

Why is der Kreuzung in the dative case here?

Because stehen in a static location plus the preposition an takes the dative. Kreuzung is feminine (die Kreuzung), so in dative the article becomes der.

Why do we say viele Studenten and not viel Studenten?

viel is used with uncountable nouns (viel Wasser, viel Zeit). For countable plural nouns you use viele, so you get viele Studenten (“many students”).

How do we know to use the adjective ending -e in die richtige Richtung?

Richtung is feminine and here it’s the direct object (accusative). After a definite article (die) an attributive adjective takes the weak ending -e, giving die richtige Richtung.

Could we say suchen nach der richtigen Richtung instead of suchen die richtige Richtung?

Yes. suchen can be transitive (taking a direct object: die richtige Richtung) or intransitive with nach + dative (nach der richtigen Richtung). Both mean “to look for the right direction,” with only a slight stylistic difference.

Why isn’t there a comma before und connecting the two verbs stehen and suchen?

In German, you don’t put a comma between two main verbs or clauses joined by und when they share the same subject. Since viele Studenten is the single subject doing both actions, no comma is needed.

Why is stehen placed immediately after Nach dem Unterricht rather than after viele Studenten?

German main clauses follow the “verb-second” (V2) rule. Whatever you put in first position (here the adverbial Nach dem Unterricht), the finite verb (stehen) must come in second position, even if the subject follows.